Yes. To count towards your unlock eligibility, milestones must be completed before their deadline date. This includes Turbo milestones, which need to be completed faster than standard ones.
If you miss a deadline, that milestone will not count towards unlocking your next game. Make sure you keep an eye on your deadlines and prioritise completing them within the required timeframe.
You can see your active milestones and their deadlines on the offer's screen.