I would say "rose" which is past tense. ("So did spending" is a reference to the past). The present tense would read: As profits rise, so does spending.

Here's how to solve it. What tense is the second verb "did"? The first verb needs to match it.

Look at the tense of the second part of the sentence. What tense is it? This will tell you the answer. Only one of those verb forms is in the same tense as the rest of the sentence. (Note to fellow answerers - please let Ir L work this out for himself!)