@TeddyBearBonfire reported this in this forum post :

Hmm, nevermind, NEOS itself isn't the issue. It seems it's an interaction with Kerbalism after all. I tried it with only NEOS, KAS, and KIS, and it worked fine, added back in Kerbalism and it worked in a save with the test already completed prior to reintroducing Kerbalism, with just reentry to go, but didn't work on a save where the test was still to be performed with Kerbalism. I wonder if it's because of the way Kerbalism stores science—since in the save with the test already completed I'd presume the data is stored the normal vanilla way, but the save where the test still had to be performed with Kerbalism would inevitably go through Kerbalism's data storage system (very much a layman's guess ;) ).

Still an issue on KSP1.6.1 with Kerbalism 2.1.2. Kerbalism author has so far failed to respond to any of the issues raised on his bugtracker about this.

Marking Kerbalism as incompatible with NEOS in CKAN for now.

The next version of Kerbalism will honour the dataIsCollectible flag, which KEES experiments set, so that should resolve this issue.
Keeping this open until their release to remind me that I have to update the .netkan again.

Further information to troubleshoot :

Oh nice, didn't think you'd be fussed about intermod compatibility—that's cool. I made a bunch of saves while messing with it. I tried with POSA1, with PPMD, and just out of curiosity I tried the Kemini (not KEES) TEST experiment too. Kemini's TEST works fine, but neither KEES completes if Kerbalism was installed while the experiment was done.

I have a bunch of saves, just threw them all in a RAR for your flexibility. Will have to explain a little though: Saves titled KEES TEST are testing POSA1 in particular. All saves made with Kerbalism installed are simply numbered, i.e. KEES TEST 1, PPMD TEST 2, etc. Any save made without Kerbalism installed is numbered V1, or V2 (V for vanilla, even though it's not strictly vanilla—minimal mods essentially, just NEOS essentials)

Otherwise, they are what they say they are—KEMINI TEST is specifically the Kemini module called TEST, and PPMD is me going for another KEES test just to see if it was specific to POSA1, which it's not. I saved at frequent intervals from contract acceptance to touchdown immediately prior to recovery. If Kerbalism is installed when the experiment results are finalised, the 2nd objective will not complete on recovery. If Kerbalism is not installed at the point when the experiment is finalised, the 2nd objective will complete on recovery, even if Kerbalism is reinstalled between those two points. I've repeated this a few times now and those results come as I predict every time.

Most of the saves were just to cover all bases and help me pinpoint where the change seems to happen, have a look at these particular saves:

KEES TEST 8 SPLASHDOWN—POSA1 done with Kerbalism, should result in incomplete objective, whether you have Kerbalism at this point or not.
KEES TEST V2 SPLASHDOWN—POSA1 done without Kerbalism, should result in completion, whether you have Kerbalism at this point or not.
KEES TEST 6 ORBIT PRE-FINALIZE—this is the branching point, if you want to try for yourself with and without Kerbalism. This will load as POSA1 has filled its timer and just needs to be finished.

PPMD TEST 4 TOUCHDOWN—PPMD done with Kerbalism, should result in incomplete objective, whether you have Kerbalism at this point or not.
PPMD TEST V2 TOUCHDOWN—PPMD done without Kerbalism, should result in completion, whether you have Kerbalism at this point or not.
PPMD TEST 2 PRE-FINALIZE—As above, the branching point but for PPMD instead.

I also included my Kemini TEST run, but since it worked fine with Kerbalism I don't know if it'll be of any value. There are no non-Kerbalism saves with that one since it worked.

https://drive.google.com/open?id=1HbB1qvgY-Gqp9c-ZNj6ojx9J5rJavtJr

Does the log flush itself out with every session of the game btw? I've not used it before, I was going to share it but I think I've lost the log for those sessions I just did because of restarting KSP a few times. If the saves aren't enough on their own I'll see about reproducing those runs to get the log—it's the file named KSP in the parent installation folder, right?

Anyway, hopefully that's useful, cheers. :)

2018-10-23 KEES Kerbalism Issue.zip

Fixed in Kerbalism/Kerbalism#249