RosterApps tracks every action that happens on every shift it has listed. Any employee-based action that takes place on your shift will require your authorization or initiation. So, if you trade one of your shifts to a co-worker in exchange for one of their shifts, this action will be tracked and logged in the History of any given shift. In the case where you initiated the trade, RosterApps assumes that you know what you are doing, and does not require your authorization to proceed. If a co-worker initiates a shift transfer or exchange with or to you, you will be required to either accept or deny such transfers or exchanges.
In the event you have exchanged a shift with a co-worker and cannot remember who it was, you can look on your calendar. Find the shift that you exchanged, listed on your schedule (most likely) with a CYAN (or light blue) color on it's left side, which denotes that the shift was received by you as a trade from a co-worker. Left-click on that shift, and select 'History' from the pop-up menu that appears. The resulting page will be a History of everything that has happened to that shift, including where it came from.
If you have given your shift to a co-worker, and cannot remember whom you gave your shift to, you may want to consult your Supervisor who can run a Trades report to determine who received your shift.