Should RTM amplitudes (pre- and post-stack) be related to rock physics properties?
It depends on the implementation, but bare-bones reverse time migration is usually not amplitude friendly.

The problem is that the ideal imaging condition — deconvolution — is difficult to apply or unstable in the time domain. So cross-correlation is used instead, and this loses the relative amplitude information... so amplitudes are no longer necessarily related to reflection coefficients. Since this is the assumption of inversion (e.g. AVO inversion), an RTM volume could give spurious results.

Several vendors have devised ways to compensate for this. For example, Zhang &amp; Sun (2009; First Break, vol 26) described one of CGG's methods. Zhang et al. have written more recently (2013; EAGE London) about how this processing has evolved. Cogan et al (2011; SEG Annual Meeting) have written about Schlumberger's normalization algorithms, which aim to achieve the same goal.

Those papers also contain nice explanations of why RTM is not ordinarily amplitude friendly.

My advice is to talk at length to your vendor about the processing applied, and the attention paid to phase and amplitude. Ask lots of questions. Most processors (generalizing horribly) are either over-enthusiatic about treatments, especially new and/or proprietary ones, or ignorant of your needs as an interpreter–analyst. So if you're actually in the middle of processing now, test everything, ideally against geological data (like a synthetic).

Lots of processing steps can hurt amplitudes, and inversion can work in surprisingly poor data... so assume nothing, and never give up!