Multiple users can be in the plugin at the same time, processing transactions. It's OK for multiple users to be within the same transaction link, for example Donations, processing transactions at the same time. 
When user A has a transaction selected in the plugin, the system Checks Out the transaction and makes it unavailable for processing by other users. The Process button may gray out​ and prevent it from being processed. 

Alternatively, you may see an error message if trying to manage the transactions:
Error: One or more of the transactions selected were not deleted. You may not have sufficient rights to delete the transaction - when deleting transactions in the plug-in

Use assignments to limit who can process certain transactions