From the Legacy manual on monsters:
Monsters make a Speed roll at the start of their turn to determine their moves (minimum of 1). This applies to all monsters of the same type.
Monsters don’t take damage from tile effects.
From the Legacy manual on trait rolls:
You will often be told to make a trait roll based on one of your family’s traits (for example, “Make a Might roll”). When that happens, roll dice equal to the number you currently have in that trait. For example, if you must make a Sanity roll, and you
currently have a Sanity of 4, roll 4 dice and total the dots together to get the result. The card’s or tile’s text will tell you the outcome.
As you mentioned in the comments, this text was deliberately changed from the non-legacy game that used to say "monsters can ignore any harmful text on a room tile." I am assuming that by environment you mean it was an Ongoing Event, which monsters never ignored, not even in the non-legacy game.
I do not think there is an answer for your question on the manual, not on the legacy manual nor on the non-legacy manual. I'd suggest your group house-rule this in one of the ways:
- Make all monsters affected by the Ongoing Event even if only one is inside it.
- Make two different speed rolls for movement, one for Monsters inside the Ongoing Event with speed minus 1, and one with base speed for Monsters outside.
I'd go with 2 because it just seems fairer and makes more sense. The manual itself acknowledges not everything is covered there because that'd be hard with all the cards.
Betrayal games mix effects on cards, haunts, rules, and tiles to create interesting combinations. We have tried to make it easy to understand how all these different effects might work together. However, the nature of the game means that you will inevitably find combinations that create uncertainty. In addition, legacy games create higher stakes since some effects are permanent. Here are a few guidelines when faced with uncertainty:
- Rules in haunts trump other rules.
- Rules on cards or tiles trump rules in the rulebook.
- if you find a single card, rule, or effect that gives you a wildly powerful moment, >that probably isn’t its intention.
- If you find a combination of several cards, rules, and effects that give you an
advantage, that probably is the intention.
- If an effect seems wildly unfair, that is not the correct interpretation.
Although it is a game of murder, insanity, horror, and other savagery, be mindful of other players’ experiences as well. Arguing about rules loopholes isn’t horror, it’s horrific.
This seems a fair application of Rules on cards or tiles trump rules in the rulebook.