Yes it absolutely sounds accurate. In fact it is exactly what we expected to hear, based on the noises and change in engine operation you described. Those are textbook symptoms of an engine coming out of time.
What he means by "jumped time": this means a timing belt or a timing gear slipped, due to the installation having been screwed up. It's not something that just happens for no reason. It's because a mechanic got belt tension wrong, or incorrectly installed a component, or didn't correctly torque one or several of the camshaft or crankshaft center bolts causing one of the three timing gears to slip. Commonly seen reasons why these things would happen are attempts to do the job without the correct tools, the correct information, the correct experience, or without all three.
The key question now is whether it jumped time on the camshaft timing belt, or the injection pump timing belt. These engines, like many others, have both. Jumping time on the IP belt will cause the engine to run poorly or not at all, but doesn't lead to long term harm. If that's what happened, then you got lucky. However, jumping time on the camshaft belt, like on any diesel engine (and almost all gas engines as well), is a major deal that always results in internal engine damage. If that is where it came out of time, then the engine needs to be disassembled again and probably will need another cylinder head rebuild, at minimum.
Needless to say, cross your fingers for the lucky scenario. But regardless, the fact that this happened should serve as a warning about all the other work that was done on your engine. More problems could occur for similar reasons of incorrect technique and/or equipment, and some of those other problems could be much more catastrophic, destroying the engine or even putting you as the driver in danger.
Before having your mechanic go any further, you want to ask some friendly questions.
Start with these:
1) What was the technique and specific tools used to install the front bolt on the crankshaft? And what torque spec did he use on that bolt? Sourced from what information? Best would be to ask him to send you a photograph of the tools he used, and then post that here. This will tell us, and you, a great deal.
2) Which belt does he believe slipped? And why did it occur, from his point of view?
3) What is his plan now for fixing it such that it won't happen again? What does he intend to do differently this time?