You are mistaken and this is an excellent question to understand a small portion of the "Main Evaluation" that happens in every single Mathematica call. Let's start with a very simple expression

Print[1+1]

Why do you think Mathematica prints 2 and not 1+1, because this is what I told it to do? The answer is that the standard evaluation chain (read: the function does not handle its arguments in a special way), Mathematica always evaluates the arguments of a function before it calls the function. This means here that first 1+1 is evaluated to 2 and then Print[2] is called.

Now look at your example and you understand easily, that you are searching your error in the wrong place. Let us assume, you have called your first line test0[..] then a has a value of 2. Now, apply the same rule I described above to the line

test0[2, test1[]]

What do you think happens if before test0 is even called, its arguments and especially test1[] is evaluated. Do you see, that test1[] does evaluate to 2? Therefore, your Return line just gives the constant value 2 and not the result of calling test1. The third result works the same way but in the meantime, you have assigned a new value to a.

To solve this, you have to force Mathematica to keep your test1 argument unevaluated

test0[1, Unevaluated[test1[]]]
test0[2, Unevaluated[test1[]]]
test0[3, Unevaluated[test1[]]]