I have 2 journeys. One is the welcome journey, and one is the post-purchase journey. We automatically opt-in all users who checkout. Unfortunately right now new all users who checkout with us are getting BOTH the welcome and post-purchase journeys. both journeys have different data extensions. We would like to have it so that if a user is a new user, they ONLY get the Welcome Journey and do not get the Post Purchase Journey.
As it has been considered already in the comments, you are probably using the same Entry Source for both Journeys and/or do not have any entering rules for the Journeys.
To start segmenting people when they enter, you can create an additional field in the Entry Source Data Extension, which would symbolise whether a contact is a new user, e.g.
Field NewUser = "True" and then add a filter for the Entry Source for one of the two Journeys, which would filter out people who (do not) have
Field NewUser = "True".