I think the idea is you watch the movie however you like/can and then post to the #MondayActionMovie hashtag on Mastodon at the scheduled time, along with everyone else (who are watching it at the same time).

As @[email protected] said

• prepare to watch the movie itself whatever way you can/want (your own physical media, locally stored file, whichever streaming service offers it in your area)
• everyone starts the movie when the ‘host’ posts “press play now” on Mastodon
• participants proceed to post about it on Mastodon, including in their posts the hashtag #MondayActionMovie (and sometimes also a hashtag with the name of the movie)

For #MondayActionMovie, the rotating ‘host’ of the party (the person who chooses the movie) often includes a streaming link in their Mastodon announcement or in the event details in the watch party calendar (go down to the calendar, scroll calendar to the relevant date, then find and click on the event name; a popup will show more info on the event. E.g. a copy of the movie on YouTube https://youtu.be/xxeDmjgSS1I )