ReRAM CMOS compatibility (vs phase change memory)
Compatibility could refer to any of a number to different and varying issues but mostly refers to fab poisoning.  In general the techniques and equipment used will be similar, only sometimes is a certain piece of equipment not available.

CMOS compatible refers more to the potential to "poison" the fab.  Meaning that you have introduced a material into the fab that will cause your yield to crash mainly because the new material interferes with the device operation, has nasty characteristics or is hard to control in fab.

I would caution against overly broad conclusions as the various companies that are implementing the variants of these two different devices almost certainly will be using different materials.  In general Tantalum (which is used in some ReRam devices) is a fairly benign material which forms a stable oxide that is not mobile in-situ. Additionally the technique used for its deposition is fairly safe in terms of how much material gets left in the chamber and how easily the wafer can be protected.

Phase change devices use many different chemistries/materials, I'm sure some of them would prove to be difficult materials to deal with.

As a case in point, copper (Cu) was once forbidden in foundries and it was considered to be incompatible with CMOS processes.  However, techniques were developed and now all processes below 90 nm all use Cu in the wiring.  Cu is particularly nasty in that it is highly soluble in Si (yes, solids can be soluble with each other) and a Cu atom can move 100's of micrometers per hour at room temperature in a Si substrate.  Also, application of Cu means that it is plated (an electro chemical process - not used that much before Cu) which means the whole wafer must be exposed during processing.  With Aluminum (Al - the previous metal used)) this is sputtered and only lands on the top of the wafer where it should go.

To answer your first question: "it means that ReRAM can be constructed with "standard" manufacturing processes, correct?"  No, there are many different techniques used which are determined by material composition, chemistry and nature of the films needed.  Most are available in fab. An integration engineer may not want to use a particular machine for this new material with an old one but most materials can be dealt with using extant equipment.

And your second question "... uses more "exotic" compounds and therefore ..." is the right answer if you've picked a particular Phase change device that uses an incompatible material.  There are so many variants that you'd have to specify what device is being compared.