Kim,
If you run the pump 24/7, then having constant power to the SWCG is not a big deal. When you turn off the pump for any maintenance you should also turn off the AC power to the Cell's Power Center.
Since the Pump and Cell do not share the same breaker, it is very doubtful that installing the pump had anything to do with the cell blowing the fuse. Although if they did not turn off the power to the cell, while they replaced the pump, the cell could have been damaged if the flow switch was also bad.
It appears that you have an old power center with an actually glass fuse... The whole fuse assembly is known to go bad. This will not pop the fuse, but it will make the fuse contacts intermittent. Are you sure the fuse actually blows? Did you test the "bad" fuse with an ohm meter to see if it was open?
As a test, disconnect the cell from the Power Center than turn the power on, and see if the Power Center still blows the fuse. If not, then power off, reconnect the cell, then turn the power back on and see if the fuse blows.
If the fuse blows, with the cell disconnected, then the surge card inside the Power Center is most likely bad.
Thanks,
Jim R.