Do I need to refrigerate fruit (pineapple) infused tequila while it is infusing? I haven't. Is it still ok?

I think so too. We use fresh fruits like ume plum, rhubarb, kumquats and natsu mikan--citrus, blueberries in shotchu which has an alcohol level of 35%. We never refrigerate. Keeps about a year but did find plum wine in a shed for 10 years--boy was that mellow!
Tequilla has an alcohol content of 40% or above so should be fine.

Should be fine. The high proof of the tequila will inhibit spoilage.