Well, unless I'm mistaken, a lot of talismans involve successfully completing the level given certain guidelines - I was under the impression that if you failed to complete the level, you don't get the talisman. Granted, it depends on how flexible the talisman system is.
Yes, they do. However, try the following. For the sake of simplifying things here, I'm going to use an example talisman where the rule is "Save 38 lemmings with no more than two builders".
1. Start with a save file where you have not already unlocked this talisman.
2. Go to the level that has this talisman.
3. Get to 38 lemmings saved, without using more than two builders.
4. Insta-restart the level via the R hotkey.
5. Complete the level; it doesn't matter whether or not you meet the talisman requirements during this attempt.
The result...
You don't get any special message on the postview screen. However, if you check the Talismans menu, you will see that the talisman has indeed been unlocked.
Now of course - this is probably best defined as a bug that needs to be fixed. But if we have multiple talismans in the single level - not something that's happened yet as far as I know, but definitely something the game allows for and as mentioned, I'm considering doing so in a future pack - then this would be a good reason to perform steps like the above. But this hinges on you knowing that you do still get the talisman awarded, even if you don't get a special message for each one. Going on from this; I would also argue that if you didn't get a notification as soon as the talisman was unlocked, you may not realise that you get it awarded even if you don't go to the postview screen (indeed, you should - assuming NeoLemmix does save your progress in such a case, which it should do but I haven't tested - get the talisman even if you replace step 5 above with "Exit NeoLemmix by pressing Alt+F4"; the postview screen has nothing to do with unlocking talismans beyond displaying a message stating that you got one).