It’s buffable either turn. The “base” part of the text just means it only affects the printed stats on the cards, and not other effects like counters or anthem abilities. So this creature with a +1/+1 counter is 6/3 on your turn and 3/6 on an opponent’s turn

It is still buffable on your turn, but the buff will apply to the stats of 5/2.

So if you enchant it with something that gives +2/+0, it will be a 7/2 during your turn, and a 4/5 during theirs