In any question about relativity you need to specify all the details, including who is measuring the clock and how.
In general the slowdown of a moving clock relative to an observer deemed "stationary" is independent of direction. All that matters is the relative speeds. This means it is symmetric between observers: if A calculates B's clock to be slow (based on say the frequency of received signals and correcting for the finite speed of light) then B will also observe A's clock to be running slow in exactly the same way. See How can time dilation be symmetric?
It is important to emphasize that this conclusion is supported by over a century of experiments and observations. The theory of relativity is not some new and speculative conjecture. The predictions of relativity are surprising and counterintuitive, which is why physicists tested the theory before accepting it.
EDIT: Here's a concrete example. Consider two space stations A and B located 10 light-seconds apart in deep space, at rest relative to one another, and with clocks carefully synchronized via exchange of radio signals. Alice leaves space station A, traveling at 0.8c (relative to the stations) to visit Bob on space station B. Her clock transmits a signal once per tick. How often is Alice's clock ticking as observed by Bob?
In Alice's frame the events of the clock ticks have coordinates $(t',x') = (0,0), (1,0), (2, 0)$ and so on. We use the Lorentz transformation to find the ticks in Bob's frame to have coordinates $(t,x) = (0,0), (1.67, 1.33), (3.33, 2.67)...$. Those are when and where the broadcasts occur. Due to the finite speed of light Bob doesn't receive the signals until later. For example, Bob is 10 light seconds away so the first signal is received at his coordinate $(10, 10)$, the second at $(1.67+(10-1.33), 10) = (10.34, 10)$, the third at $(10.67,10)$ and so on; Alice herself arrives at station B at the event $(12.5, 10)$ since it takes her 12.5 seconds to travel 10 light-seconds at 0.8 c.
Some things to note here:
(1) Bob is actually receiving Alice's signals at intervals of 1/3 second; that is, if you consider what Bob literally sees with his eyes, he sees Alice's clock ticking 3 times per second (much faster than his own).
(2) However, Bob is a smart guy and knows that the speed of light is finite. If he works backwards from when he sees the signals to when they were actually emitted, he works out that Alice's clock is actually ticking slower than his clock (only once every 1.33 seconds).
(3) All of this is completely symmetric. If Bob's clock is also broadcasting once per second, with spacetime events in his frame of $(0,10), (1, 10), (2, 10)$ and so on, then Alice will literally see his clock ticks (as in receive them) 3 times per second, and will calculate that Bob's clock is ticking once every 1.33 of her seconds.
(4) How is it possible that each calculates the other's clock to be ticking slow? Because they're measuring different things. In Alice's frame she is stationary and Bob's clock is moving, so Bob's clock ticks happen at different places. In Bob's frame he is stationary and it is Alice's clock that is in different places. The link above has more details.
(5) The Lorentz transformation predates Einstein and is thoroughly tested by experiment; see for example https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_violation . Einstein's contribution was to find a simple explanation for why the Lorentz transformation works.
