new managers

Private User - Geni is probably the wrong platform for you if you cannot stand having strangers changing anything on your tree. But give it a try.

If you click on the name in blue Geni will take you to that person's profile - and show you at the top your relationship to that person. Maybe they are your third or 4th cousin and you two would enjoy sharing info.

Geni considers anyone that is 4th Cousin or closer, and their spouse, to be in a profile's Max Family. These folks can see and edit a Profile even if it is Private.
And these folks can add themself as a Manager of a Profile if it is Private.

Folks also get added as Managers when Profiles are merged, the merged version inheriting all the managers from the versions that were merged.

If you are in the Max Family of a Profile, you can remove as Manager any Profile that is not in its Max Family.
Go to the Profile.
Click Actions in upper right.
Click Manager Options
Look at the boxes with the names of Managers.
If there is an 'x' in the Box, you can remove that person as a Manager by clicking the 'x' and then confirming you want to remove that person as manager.

However, it might be worthwhile first checking if the person is active and has been adding useful documents and comments and/or asking them why they are interested. Could be somebody you would really enjoy working together with on these folks.

Thanks, was not sure that people can just jump into my tree. Hopefully they don't change anything close to my immediate and extended family.

Private User
Geni will practically always tell you when somebody makes a change to a profile you manage or follow or that is in your close family.
My practice, when I see a notice of such on my Home Page is to click on the Profile that was changed, then click on its Revision Tab to see what was changed.

If the Revision Tab shows no change, even tho Geni said it was updated, in my experience that means the person went into the Data Conflict Resolution Screen and chose the value already being used.

Sometimes I see the person corrected an obvious typo. Sometimes in the Overview's About or the Event's About there is an explanation for the data added or changed, or a document was added supporting it - or the change may have been adding an interesting Comment to one of those Abouts..

If the person has made a change - such as adding a date or place of birth - when I see no info supporting that - I will send them a PM asking where they got the info.
Other times I may start a Public Discussion from the Profile about that topic.