As other answers have pointed out, this is almost certainly a scam - there are some nuances to the "sugar daddy" aspect, but there are also some very obvious red flags.
Insistence on transfers via specific methods. Some non-scammers may be picky about how they transfer money, but scammers are almost always interested in forcing transactions via specific channels, because they believe these channels will allow them to be more successful. In other words, the scam doesn't work if they use paypal.
Sudden change in terms that involves "extra" money, which you're supposed to send somewhere else. The fact that the daddy suddenly sent you extra money and wants you to send it somewhere else is a red flag. People behaving legitimately have no need for a middleman to move money. Ask yourself this: If the daddy is capable of sending you money, and can describe to you how to send it to this caregiver, why can't they just send it to the caregiver themselves?
Questions about personal details that aren't relevant to the relationship - he asked about your address and didn't have a good reason why. That's a red flag. Him having your address would have likely allowed him to further the scam, since it's something he can use to impersonate you or steal from you - for instance, if he phoned your bank and tried to pretend to be you, knowing your address (and other things like your account number and/or birthdate) would have allowed him to do a better job of convincing the bank that he was really you.
Generally, these scams play out in one of two ways:
The money was never "real" and you'll soon find that their deposit into your account has been reversed. If they send you $1,000 and tell you to send $500 somewhere else, and then the $1,000 disappears after you have sent out the $500, the bank will come after you for the missing money. You will be $500 poorer, and the scammer will have made an easy (and likely unrecoverable) $500.
The money is real but it is "dirty" - the scammer may be a criminal or a terrorist, and may be sending real money through you as a way to launder it. In that same scenario, they may be happy to "lose" the $500 you kept, in order to have a "clean" $500 deposited in a different account - money laundering is a cost of doing business for criminals, and at the end of the day, if or when they are found out by law enforcement, you will be the one who gets in trouble - the FBI will come knocking on your door.
The second version has another common variation, too, that's more or less a pure kiting scheme and not based on laundering money they obtained somewhere else: The money may be "real" but from a stolen account. If this scammer is scamming several targets, they may have access to several real bank accounts with balances. What they typically do is shuffle money between their targets as a way to wash it. So, if they deposit that $1,000 into your account, that $1,000 may simply be them stealing money from another target. Ultimately, then, the $500 they ask you to move somewhere else is the percentage they're keeping for themselves. If they ask for your bank credentials (i.e. username and password to get into online banking) this is almost certainly the version they're following.
It's notable that sugar daddy dating websites and other romance-related social media are common scamming targets. This is because people on these websites are often so interested in participating in these social constructs that they're willing to ignore red flags. Also, it's common in sugar daddy relationships for money to be flaunted, and for money to change hands "easily" as a way of showing off - so, people who are victims of these scams may not be put off by "someone they don't know" suddenly sending them a lot of money, whereas the general public may be skeptical of "free money."
At the end of the day, Is this a scam? is only the first question you need an answer to. The second question is, what should I do?
If you've identified that you're the victim of a scam, you should:
Notify your financial institution. If you have sent or received money, or you have shared any details about your bank account or any method to access it (i.e. online banking credentials, a mobile banking app, etc). you should notify your bank immediately. They can help you determine what you need to do to be safe. It sounds like you've given at least some information to the scammer since you mentioned changing your password - even if you think you can keep yourself safe by changing a password or closing an account, you should mention the scam to your bank. Scammers sometimes target specific channels, or even specific financial institutions, since they believe they can be more successful that way. For instance, scammers will sometimes ask their target to open a new account at a specific bank, because they know the triggers that bank uses for mobile check deposits, or online banking transfers. Banks need to know about scams in order to help protect people against them. Even if you can keep yourself safe, informing your bank will help keep other people safe.
Inform the online community via which you met this scammer. You mentioned that you met the daddy on a sugar daddy dating website. That website may be interested in taking action against this scammer - at the least, blocking their account. But, they may already have a strong law enforcement relationship, and informing them of the scam will help them either track the person down, or prevent future scams (by introducing controls in their web platform, or tracking the person's IPs or taking other investigative actions).
Spend some time learning about common scams and how to avoid them. Regardless of what happens with this daddy, you should recognize that participating in sugar daddy relationships online is very risky due to the frequency at which they involve scams. Educating yourself on this scam, and other common scams, will help prevent issues in the future. Your instinct to use a secure payment method was important and should not be ignored. Talk to your financial institution, they may have educational programs or materials you can review to help you understand what you can do to keep your finances safe.
