I agree with the above comments that you're very unlikely to have problems as long as you take advantage of opportunities along the way to let the tent dry out. I've frequently had to pack up a tent still rather wet in the morning and it's never resulted in a mildew problem since I don't leave it packed that way for more than a day. The OP mentions plans to stay in homes or hostels some nights and that should provide opportunities to hang the tent in a dry storage area even if there have been a series of wet days.