It's quite common for images that are entirely in gamut to soft proof and print differently between Relative and Perceptual Colorimetric.
Relative Colorimetric Intent is well defined for all in-gamut colors by the ICC. However, Perceptual Intent for printer profiles is not. It's up to the creator of the profiling software. Colors that are in gamut and accurately printed using Relative Colorimetric intent are almost always shifted when using Perceptual to allow room for compressing highly saturated colors. Also, vendors of ICC profiles often increase saturation so that a print appears more colorful. Both of these effects can be seen in the OEM ICC profiles for the Canon Pro1000 printer with glossy paper (Canon PRO-1000/500 Photo Paper Plus Glossy II A).
This charts shows the actual printed a* (from Lab* where L* is fixed at 60 and b* at 0 while a* is varied from 0 to 100, The printer's gamut is limited to approx a*=80. The printed a* in Perceptual is more saturated (44 v a requested 40) below 70 but reverses and becomes more compressed when nearer the printer's gamut limit. For instance when requested to print a*=80, which is right at the printer's gamut boundary and printable in Relative Colorimetric, compression reduces the printed a* color to 73. However it prints at 80 using Relative Colorimetric.
So, as we see here, there will be a discernible color shift for many colors well even when those colors are well inside the printable gamut.