In general: Yes, Customs Duties Apply!
Anyone importing anything is required to declare the item for calculation of customs duties. There are the tariff and taxes one needs to pay to bring an item over the border, as soon as the item transported qualifies. The key point here that tariffs are a tax on importing goods, and that the duties are calculated at the point the wares cross the border.
Do note though, that for many products some minimum amounts or values need to be imported before the duties are collected - these are also known as "small amount" and "personal duty-free" amounts, and most are listed under the exemptions to a tariff. Those duty-free amounts are setable by the secretary of the treasury under 19 U.S.C. ยง 1321. This law also explicitly dictates minimum values to be allowed to collect duties in (2) - 100 USD for gifts, 200 USD for carry-on goods or household use, 800 USD in "any other case". Also, (3) bars collection of duties below 20 USD.
Resellers usually pass on those costs by increasing the price they charge to people who purchase goods they import from them to cover this cost.
Examples
Postal Import
If Alice from Eagle Pass, Texas, orders eggs from the supermarket in Piedras Negras, Mexico, just a few miles away, and they get delivered by post, then the parcel needs to be taxed, and tariffs paid as soon as the minimum tariff value is met.
Note that tariffs and taxes apply to the combined value of product and shipping, not just the product value. So, assume that customs duties are 50% of the total (product + shipping) price. This is a currently hypothetical, very much inflated rate, but makes math easier. Also, we'll assume that the duties fall half to the tariff and half to other taxes (such as VAT). What happens is that:
1 dollar per tray of eggs plus 4 dollars shipping is 5 dollars, so this would add $2.50 in duties, $1.25 each for taxes and tariff, brining the total cost to $7.50. But, this value might not be enough to trigger the minimum required amount to require the payment of the customs duty, and thus might fall under a "small amount/personal use" exception.
For most products, the value of duty-free shipping can depend on the origin - insular possessions of the U.S. have a 1,600 USD (i.e. U.S. dollars) duty-free amount, and Andean countries 600 USD. Atop that, the first 1000 USD above those minimums (until last month) owed a 3% flat duty overall, but that might change soon.
Import when crossing
The same percentage of tariffs and taxes apply to the eggs if Alice drives over to Mexico to buy her eggs. Legally, she is required to declare them at the border, and we'll assume that eggs are an importable good for this calculation.
Assuming the tray of eggs costs 1 USD in Mexico, and knowing that there is no postal fees that demand duties, she has to pay eac 25 cents taxes and 25 cents tariffs. Thus she'd have to pay (overall) 1.50 USD for them in her luggage.
This presumes that such small amounts of dues are collected in the first place, and that there is no personal use exception. On many products, there is a personal use amount for tax-free importation on your person - such as the "200 USD personal effects", which applies (among others) for short stays of less than 2 days and repeated crossing. In general, personal transport with you often has higher duty-free values than getting it by postal services - especially since the transport is not part of the value that is taken into account for duties.
Buying from an Importer
Now, if Alice goes to Bob's supermarket in Texas, and Bob stocks the eggs from Piedras Verde, then Bob already paid the import taxes and tariffs, as Bob is the importer. However, he also will add those costs to his base price, and only then calculate his margin when Bob sets the retail price he charges to consumers. A very typical margin for food items sold as groceries is selling at 3 times the base price.
So let's say Bob paid 1 dollar for a tray of eggs including shipping (bulk orders make that possible), that gives us 25 cents extra tariffs, and 25 cents normal tax, that's the same $1.50 base price Alice would have paid personally importing in her luggage. This gets multiplied by 3 for margin, so $4.50 per tray in sale. Without the 25% extra tariff, but only the normal 25% taxes, the resulting sales price would be $3.75.
