Cyclocross tyre patching problems, bulging inwards
If you inflated the tire and the tire itself is indented at times, it is likely that you did not seat the tire correctly.  This means the tire bead is not sitting correctly in the rim.  The rim should have hooks to catch the tire bead. The tube should expand to many times its original size and will fill the volume made available to it.  As such, a tire that is not seated properly will present a different radius to fill making it look like the tire is indented.

Try deflating the tire so that is has a very low pressure then squeeze and pull on the tire to try and get it to seat properly.  Re-inflate, then check.

Also sometimes a high pressure can make the tire seat correctly.

Finally, if your rim tape has slipped it can interfere with the tire seating correctly.  Check to make sure the tape is in the proper location.