I'm making an iOS dice game and one beta tester said he liked the idea that the rolls were already predetermined, as I use arc4random_uniform(6). I'm not sure if they are. So leaving aside the possibility that the code may choose the same number consecutively, would I generate a different number if I tapped the dice in 5 or 10 seconds time?
Your tester was probably thinking of the idea that software random number generators are in fact pseudo-random. Their output is not truly random as a physical process like a die roll would be: it's determined by some state that the generators hold or are given.
One simple implementation of a PRNG is a "linear congruential generator": the function rand() in the standard library uses this technique. At its core, it is a straightforward mathematical function, and each output is generated by feeding in the previous one as input. It thus takes a "seed" value, and -- this is what your tester was thinking of -- the sequence of output values that you get is completely determined by the seed value.
If you create a simple C program using rand(), you can (must, in fact) use the companion function srand() (that's "seed rand") to give the LCG a starting value. If you use a constant as the seed value: srand(4), you will get the same values from rand(), in the same order, every time.
One common way to get an arbitrary -- note, not random -- seed for rand() is to use the current time: srand(time(NULL)). If you did that, and re-seeded and generated a number fast enough that the return of time() did not change, you would indeed see the same output from rand().
This doesn't apply to arc4random(): it does not use an LCG, and it does not share this trait with rand(). It was considered* "cryptographically secure"; that is, its output is indistinguishable from true, physical randomness.
This is partly due to the fact that arc4random() re-seeds itself as you use it, and the seeding is itself based on unpredictable data gathered by the OS. The state that determines the output is entirely internal to the algorithm; as a normal user (i.e., not an attacker) you don't view, set, or otherwise interact with that state.
So no, the output of arc4random() is not reliably repeatable by you. Pseudo-random algorithms which are repeatable do exist, however, and you can certainly use them for testing.
*Wikipedia notes that weaknesses have been found in the last few years, and that it may no longer be usable for cryptography. Should be fine for your game, though, as long as there's no money at stake!