What do phase dots on an inductor mean?
If we're thinking about same thing, then dots show relation between coils. Here's an article about that. 

If I get the dot relation correctly (and I'm not sure that I do), if current is going into the dot on one side of the inductor and the other dot is on the same side of the inductor, that means that current is going into the dot on the other side too.

How important it is to have dots in the same place is up to design of the circuit. In some cases it may not be relevant, but often it is important to take it into account.