Not sure I understand the question correctly, but it seems you may need a My Heritage data subscription for that.
For transferring tree data you can use SmartCopy (see https://www.geni.com/projects/SmartCopy/18783). You can also use it help see data conflicts and other data problems use it to add a biography to profiles.
An "orange Save button at the bottom of records" -- you are referring to "Save Record" after the words "Save this record and extract info to a person in your family tree" - yes? That is on MyHeritage and has nothing to do with Saving the Record to your Computer.
Ancestry explicitly asks if you want to Save to your Tree or your Computer.
MyHeritage just uses to refer to your Tree.
To save an actual image of a record on MyHeritage - on my Tablet I have to hold my finger down on it till a pop up window appears, then choose "Download image" from the window.
For the Orange data records from My Heritage on Geni that are not free (some are free) you need a separate My heritage data subscription (that has nothing to do with your subscription you have for your My Heritage tree). Many of those records are also available for free but it take (sometimes much) more effort to find those free records.
See https://help.geni.com/hc/en-us/articles/229707427-What-is-a-MyHerit...
Don't know if this still works: https://www.dallascountygenealogy.com/myheritage-data-subscription-...
This is what My Heritage has as info about it: https://faq.myheritage.com/en/article/what-is-a-data-subscription
If you want to take it you could choose a date (like Black Friday) when there will probably be a discount. You can see likely dates from the Geni translations (those offers have to be translated into other languages), see https://www.geni.com/tr8n/phrases?section_key=&source=&search=discount&phrase_type=any&phrase_status=any&phrase_lock=any (you may have to change your language to see)
If you have a MyHeritage Complete Plan that includes the Data Subscription.
You still have to DOWNLOAD the record to your Computer, then Upload it to Geni.
Save on MyHeritage just connects it to your Tree on MyHeritage - or does that not work for you?
Job - Record Matches on Geni are Brown.
Do not think she is talking about Confirming Record Matches.
Do not see the word "Save" used with Record Matches on Geni.