Learn Polish: Kobiety podróżowały tydzień temu.

Because the subject is kobiety (women). Polish has two plural categories in the past tense: virile (for groups with at least one man) and non-virile (for groups of women, children, animals, or objects). Since a group of women is non-virile, the verb takes the -ły ending. If it were a mixed group or just men, it would be podróżowali.

I learned that verbs ending in -ować change to -uj- (like podróżują). Why isn't that happening here?

That -uj- change only happens in the present tense! The past tense is actually much simpler for these verbs. You just take the dictionary form (podróżować), drop the final -ć, and add your past tense ending (-ły).

If I wanted to say 'They traveled a week ago', which word for 'they' would I use instead of kobiety?

You would use one. In Polish, one is the non-virile word for 'they' (used for groups of women, children, and objects), which perfectly matches the -ły verb ending. You could say: One podróżowały tydzień temu. The virile 'they' is oni, which pairs with -li endings.

Does the word temu (ago) always come after the amount of time?