Selected Answer
Once an answer is "selected" a question is deemed closed, meaning there is no more need of solutions to the problem and no one else will comment. This case appears different.
When VBA is invoked Excel cedes control to it. That means that Excel functionality will be interrupted until the VBA code has run its course. At that moment control of the CPU is returned to Excel.
The Timer is not a VBA function. It belongs to Windows. Windows will interrupt both Excel and VBA to do whatever it needs doing. Take note that setting the timer doesn't mean that VBA is "running" for longer than it takes to record the set time in memory - an unnoticable fraction of a second.
However, the Timer will start a VBA procedure which will temporarily discontinue Excel functionality while it runs. The duration of the interruption depends upon how long VBA will be busy.
So far the facts. Now for conjecture. I guess that the hold VBA has on the CPU doesn't extend to other applications. You might try whether a document open in Word is affected by a macro simultaneously running in Excel. If there is no interference the solution to your problem would be to run your On Timer macros in a separate, dedicated instance of Excel.
Yes, you can load several instances of Excel simultaneously on the same computer. MS Office doesn't expressly delegate the choice of instance to the user. Quite to the contrary, Office will decide in its own mysterious ways whether to use an existing instance or create a new one. Sometimes this leads to confusion when you can see that two documentds are open but they cant "see" each other. That's when they are open in different instances of the application.
Using VBA, however,it's simple to create a new instance (use the New keyword). To implement that idea you would need to open the other workbook first and then use code to open the workbook with the On Timer macros. Any further workbooks would then be opened in the instance of the workbook that is active when you open them.