Why did I die as Tryndamere in the fountain?

Yesterday I was playing Tryndamere top. We had a large advantage and managed to destroy everything up to the nexus tower. During the final minutes of the game I decided to fountain dive the enemy Lux that just respawned but despite activating my ultimate, I died really quickly.

Isn't Tryndamere's ultimate called Undying Rage?

In the wiki it says: Tryndamere becomes completely immune to death for 5 seconds, refusing to be reduced below 30/50/70 Health and instantly gaining 50/75/100 Fury.

So why did I die in the fountain? Shouldn't I be unkillable for 5 seconds?

The fountain will attack using a beam that deals 1000 true damage every 0.5 seconds. This beam will ignore most immunity effects including Tryndamere's ultimate. Note that the damaging beam will also ignore shields and revival effects.

The only effects not ignored are the following:

• Untargetability (Fizz E, Vladimir Pool)
• Stasis (Zhonya's, Bard R)

And aggro can be traded like usual, meaning champions that go untargetable are dropped from the turret aggro table as usual.

Source