Q: When buying a grocery item, do we also need to be solving the corresponding aspect type?

A: No. As always, you are allowed to confirm clue cards to the center row that do not match each other’s aspect type. It is perfectly fine to buy Fruit by confirming  a Crime card to the center (and spending $4 from your player track) while you are working to solve the Object aspect. A player will simply exchange an Object card for the Crime card on a subsequent action to help finish solving for the Object.