If this were a mechanism that appeared under some kind of evolutionary pressure. What would that be? In which situations a normal mammal find its bones squished (but not crushed)? Or is it just a side effect of something else going on?

Pure speculation on a few possible explanations (noting that TFA describes ordinary exercise as generating enough squishing force, any other actions the researchers did being to isolate the causal factor):

1. Mammals don't naturally exist in environments where exercise isn't mandatory. _Some_ system had to generate those compounds, and there was never any pressure to keep it from being tied to the other stress-related changes bones undergo (like density changes). Once it evolved once somewhere in some critter once via that machinery, the advantage was large enough that it was locked in.

2. Exercise directly contributes inflammatory factors. Tying the cure to those to a measure of exercise intensity (bone squishing) helps calibrate the dosage. Even if an imperfect measure, the proxy of bone loading might confer some advantage in, e.g., not wasting energy on unnecessary proteins.

3. Exercise indirectly suggests a resource-poor environment, leading to lower chance of offspring succeeding and needing longer lives to produce enough viable offspring. The compounds in question aren't free to produce, so there's an advantage in only providing them to organisms who will meaningfully benefit. Mind you, resource-poor environments often promote shorter lifespans and faster growth cycles as an evolutionary trait, _but_ without a mechanism to force your offspring to mature more quickly the osteocyte-mediated lifespan could allow for resource-dependent lifetime offspring counts.

4. The mechanism could have evolved for unrelated reasons, perhaps directly contributing to the bone density calibration osteocytes already mediate. Any impact on lifespan is incidental or otherwise produces less evolutionary pressure for or against the feature than the direct purpose of the compounds.

5. More than having evolved for unrelated reasons, the fact that the compounds have any effect at all might not be evolutionarily selected for. We produce plenty of unimportant metabolic byproducts that we don't particularly care about, and it could be that some more important osteocyte function incidentally produces these "waste" proteins.

> In which situations a normal mammal find its bones squished (but not crushed)?

Running, exercising, etc.

I don't know if any bodily phenomena are so easily explained. The insides of a single cell are insanely complex, and to try to apply a singular causal explanation to macro phenomena seems implausible.