The M1 means your tax is based only on what you are paid in the current pay period, not the whole year. You are correct it is an emergency code.
The pension provider tells HM Revenue and Customs (HMRC) about the change to your situation. HMRC sends a new tax code to the pension provider. Once they’ve got it, they’ll use it to work out how much tax to take from your payments from the next time they pay you.
You will get a tax code notice telling you the new code. You only need to then contact HMRC if you think the new code is incorrect.