I'm a home builder down in Texas.
You will most definitely NOT have any problems using different products.
<> For example....When Sheetrock crews "Tape and Float" a house (after "hang"ing it) they will use a joint compound similar to what you mentioned you first used. It is very slow to dry, as you will usually need 1-2 days for it to dry before you can put a layer of "skim" over the first coat of float over the tape.
<>When a sheetrocker does "patch" work, they will almost exclusively use "Quick Set". This is a compound that is made to dry much more quickly. The benefit is that you do not have to wait long to then texture and paint a new patch of sheetrock.
<> <>The reason a crew would not typically use "quick set" for a whole house job is because of the material costs. Aside from that, as the damon mentioned above, as long as the prior 'mud' is dry, use whatever you want.
<> <><>As far as the vinyl spackling goes, I assume it is a pre-made mix in a tub. I've used similar products before to do "Minor" repairs. I don't believe that using it for your "skim" coat would be your best bet.
<> <><><>Go to the hardware store and ask for a "quick set" compound. It will be just like what you originally used, a powder that you mix with water. <> <><><><>If you would like some more 'tips' on sheetrock, or have more questions, I'll do what I can to help.