Does the 90-day rule make me a UAE tax resident?

Sometimes, domestically. You can be a UAE tax resident at 90+ days' presence if you're a UAE/GCC national or hold a residence permit, plus have a permanent home or a job/business here. However, the FTA generally still requires 183 days of physical presence to issue a treaty-purpose TRC, so 90 days may not secure treaty benefits abroad. (verify with the FTA or your adviser)