x2
Would have been nice to have a mass air flow reading for the rocker function while it was running. How many miles are on it now?
How many miles ago was the timing belt Engine rebuild done?
What work was done at the rebuild?
If the work was done in the last 2 years or maybe more and he did anything other than water pump and Timing belt service such as replacing head gasket he probably should have changed the rockers then . Its very difficult to tell from the pics, but if the rockers were changed recently then they should be the new style. The old style has a crimped on top portion and the new version has no crimp and at bottom has a taper to the end (actually the lifter portion). If you can't tell you could post a pic and its possible only some could have been replaced. Perhaps if you have the bill from the mechanics service it would indicate what parts we're paid for etc. Though he wouldn't absolutely have to there should be at least a charge for the intake gasket and elbow gaskets and manifold gaskets if he removed the valvecover. If he did all that and replaced the rockers too he is very reasonably priced but I suspect he only did the timing belt and hopefully water pump service. I would replace all the rockers/lifters anyway but especially if not the new type. You can definitely tell if there is rocker wear . Just hold the bearing and push on the rest if there is essentially any movement replace them. You can check several and should be able to tell some differences. If you post pic of cleaned up lifter/rocker we could tell you if its new style or not. You also need to check cam lobes for excessive wear or groving but generally this will be pretty obvious. When reassembling I recommend using bolts with cut off heads correct length to align the valvecover correctly. You will see what I mean when you get to that point I use 3 but some use 2, so you might want to order some or you can get the ones to make the guide bolts from Lowes etc. Make sure they will protrude from the intake enough to be removed. I put them only in enter holes near injector cups to enable them to be short enough to clear firewall easier and still be removable with fingers or pliers afterwards.
i know you said you changed the oil and used full synthetic but it must be Diesel Rated and Most Here do not recommend the 0w-40. Better to use at least 5w-40 or even 15w-40. for example . Do not use Mobil 1 0w-40 or 5w-40. The correct Mobil 1 product would be 5w-40 Turbo Diesel one that is sold as 4 quart containers not the 5 quart size. Many use Rotella T6 5w-40 or 15w-40 or Others.
A very important point: When you reassemble the engine use a New Timing Belt no matter how many miles are on the current timing belt !!!
make sure the previous Timing belt job replaced all Idlers TB Tensioner and water pump and if its been many miles say 50,000 miles or more I would go ahead and change those on reassembly. Remember you will need other parts to reassemble also such as seal and copper washer for injectors. These parts can be purchased separately but ID parts and Sasquatch have the Head Gasket kits that makes it easier though at times not cheaper . One main difference is some of the kits have Chrysler Head gasket and the less expensive one is sold separately for sure and the one they sell is good quality.
Double and triple check the timing pins and the crank pin after reassembly.
So clean up everything thoroughly , replace head gasket using copperkote type product using ARP studs and new gaskets etc. ,replace rockers and all valves especially exhaust valves. I recommend getting head checked for flatness and cracks also. EGR mod already mentioned and hopefully after about 12 more hours work and around $1500 to 2000 you will have a "bulletproofed" CRD engine for another 150 to 200k or more miles