Is he the best agent the government has to offer (it's my headcannon, if only cause the movies make everyone else in the government idiots), yes. Can and will this man commit acts of terror without batting an eye, yes. Does that stop him from getting triggered into an episode or flashback? No. But only inspecific circumstances.
I think being an agent has been so throughly ingrained into him that he doesn't know how to turn his hypervigilance off. He can still be surprised, of course (looking at you,Shadow), but for the most part, Stone is keyed up and always ready for action.
Except when he's with the doctor at home base. Whether that home base is the government labs, mobile lad, or the crab doesn't matter. Stone feels safe. After all, where on Earth could be safer than with the great Doctor Robotnik and his deadly machines inside a bunker of the doctors own making.
Unfortunately, with that sense of safety comes the unfortunate side-effect of the brain, finally feeling safe enough to process some horrid shit. It's not a constant problem. Stone knows the sounds of the lab. He knows when his doctor is working on something or the Badniks are wondering about.
But every once in a blue moon, something will go off. A dropped tool, a small explosion or an unexpected smashed object without the pre-warning of the doctors yelling, and he slips.
Stone has just a fraction of awareness to know who his doctor is, but the context of where they are and what is going on falls away.
He can't draw enough air, but breathing too loudly will get them killed. So he holds it. He shields Doctor Robotnik with his body while also attempting to protect his own vital spots. Mainly his throat.
The first thing he should do is remove the doctor from the area and then search for the active threat. But he just can't seem to get his legs to support him. His hands won't stop shaking enough to hold a weapon. His eyes blur with tears and leave him practically blind. So he falls, pulling Robotnik with him and covers him with his own body.
He attempts poor reassurances in between small gasping breaths. After all, it wouldn't do for the good doctor to think he would let this episode stop him from keeping the man save. Oh no. He'll gladly die for him.
It's anyone's guess how Ivo might react. He could struggle against the agent. Spouting poison about his stupid agent malfunctioning. This happened a few times early into their partnership.
Ivo could just wait his agent out. Listening to how badly Stone sounds over him. Ragged breathing, eyes darting back and forth for an invisible threat. Not knowing what to do, but understanding somewhat that fighting back could send the man spiraling further.
Or Ivo could talk. Reassuring Agent Stone of their safety. He's doing a good job. The threat is gone now, well done. He activates some Badniks to surround them as well providing his own shield. More durable than the man made one on top of him.
The episodes happen more and more often in the Crab. Once Robotnik recovered. Once they became a little more domestic as Ivo fell into depression. The number and length would very and it never failed to unnerve and frighten Ivo.
Once it passes, Stone will be embarrassed and exhausted, and Robotnik will demand the man get up and go lay down for a bit. He doesn't scold, judge, or mock. Just gives an order, easy to follow, and sends Stone for a nap.
Sometimes, Stone can't be left alone. So Ivo will turn on a movie and sit in his chair, Stone on the couch holding onto his bathrobe and watch.
They don't talk about it. Stone from mortification that it keeps happening, and Ivo because he gets it.
The brain is the body's computer and sometimes said computer can act a little funky, especially when it's been damaged. Ivo himself has had episodes that Stone has had to talk him through. He can do the same to ensure the software in Stone's head doesn't get too badly overloaded. It's the least he can do for the man.