The standard sequence in both Hac and Umre is Tavaf first, then Say. For Umre, all four schools agree that Say must follow Tavaf — this sequence is an integral part of the ritual. Performing Say before Tavaf in Umre would mean you need to redo the Say after completing Tavaf.
For Hac, there is more scholarly discussion. The Hanbali school allows some flexibility: if a haci has already performed Tavaf al-Qudum (the arrival Tavaf), they may perform Say after it. They may also, according to some Hanbali scholars, perform the Say of Hac on the Day of Arafat before performing Tavaf al-Ifadah. This is based on the hadith where Hz. Peygamber (sallallahu aleyhi ve sellem) was asked on the Day of Sacrifice about performing rituals out of order and said: 'Do it, and there is no harm.'
The Hanafi, Maliki, and Shafi'i schools maintain that Say must always follow a preceding Tavaf, whether it is Tavaf al-Qudum or Tavaf al-Ifadah. If someone performs Say without a preceding Tavaf, it is not counted and must be repeated. For practical purposes, following the standard sequence (Tavaf then Say) is the safest approach accepted by all schools. If you find yourself in an unusual situation, consult a knowledgeable scholar present at the Haram.