The correct revision should be: "We picked these apples when we went upstate, which was on Tuesday".
Explanation:
There is a small grammar problem with the sentence written in that way, basically for the comma in the wrong place, which should be written only before the last phrase "which was on Tuesday". The first two phrases "We picked these apples" and "when we went upstate" are dependent clauses and this is why they do not need any comma separating them, their meaning is established by writing them one after the other, and by the use of "when" linking both clauses. This is different for the last phrase "which was on Tuesday" that must be written after a comma because it is a secondary idea related to the dependent clauses.
