Generally with proper source control management, a person has to "check-out" a file to be able to work on it. They then make changes, and check it back in.
If person A tried to check out a file when person B already has it out, they will either only get to see it read only, won't be able to see it at all, or just won't be able to check the file back in.
Even if it allows you to both edit the file at the same time, it will store two copies when you both upload it. This is one of the main points behind version control, each edition you upload / check in, is a new version of the file. Then if you erase each others code, or if the bastardized source control lets you both check out a file, you will have to manually merge the code that was worked on.