When one is killed by a TNT that was activated by another TNT, which either was activated by a TNT or part of a chain reaction started by a player using a bow with flame, the death message do mention the culprit and the weapon (the bow).

If the initiator of the chain reaction happens to change his/her bow for another object, the message is going to display the same death message, but with the current object selected. 

In the screenshot attached, the message is displayed prompting "(...) blown by [PALAPA]".  PALAPA happens to be the name of the shovel of my friend, which he equiped after shooting the initial TNT with a flamming arrow. 

Expected behavior:

The message displayed should reference the activator of the first TNT.

Repro: 

1 - Set a trail of TNTs with a gap of 4 blocks between each TNT

2 - The victim should stay at the end of the trail. Be sure that the "victim" has low health and no armor at all, so they can die with the explotions

3 - The "culprit" must shoot the first TNT block with a bow with the Flame enchantment, and once the TNT is activated, change the bow for another tool

4 - Watch gleefully how the other player is blown

5 - Register the message.