Arduino Pro Micro clone: connect USB and RAW power at the same time?
I am unable to replicate this problem. I think you have something else going on. 



I tried every combination of 12V RAW and 5V USB power and jumper short and open using a crappy clone Pro Micro without issue. Here is what I found...

╔════════╦═════════╦═════╦═════════════╗
║ Jumper ║ 12V RAW ║ USB ║ Vcc reading ║
╠════════╬═════════╬═════╬═════════════╣
║ OPEN   ║ nc      ║ ON  ║ 4.66V       ║
║ SHORT  ║ nc      ║ ON  ║ 4.90V       ║
║ OPEN   ║ ON      ║ nc  ║ 5.00V       ║
║ SHORT  ║ ON      ║ nc  ║ 5.00V       ║
║ OPEN   ║ ON      ║ ON  ║ 5.00V       ║
║ SHORT  ║ ON      ║ ON  ║ 5.00V       ║
╚════════╩═════════╩═════╩═════════════╝


(really StackExchange, no tables?)

What is the purpose of the jumper anyway?

Although the ATMEGA32 datasheet does not seem to list a Maximum Speed versus VCC, it does show a graph with a clock speed of 16Mhz at Vcc of 4.5V...



...so this board should run fine under USB power without jumper SJ1 closed. 

I think the main reason to short the jumper would be if you were going to run under USB and needed to see closer to 5V on the IO pins rather than ~4.5V.