Clean it or not depends on attitude!
If you have even moderately hard water, minerals will collect on things and that includes the inside of tubing. So when you move the tubing while cleaning, you break the minerals loose and they do come out in the tank. So how to react? Depends on how you feel about the minerals. Some don't want to see them laying on things in the tank and want to collect it. Others have learned to be a bit more tolerant of nature and simply let it dissolve and go away.
If it is just minerals, I go for the low stress of ignoring it! In my experience, nature is rarely a pristine thing and I have learned to not expect it in my tanks as I do work to make them as natural as possible. If you want an unnatural pristine setup which would never occur in nature, you do the extra work but if you like natural, you go a bit easier on cleaning. Personal choice with no right or wrong, just do it as you feel needed.
One way to cut the mess to see is to let it come out of the outlet in a place which is out of sight behind things.