Burst life regen effects which use the "Life Regeneration" buff do not stack.

In the video the Armour and Evasion mastery - "Every 4 seconds, Regenerate Life equal to 1% of Armour and Evasion Rating over 1 second" and Enduring Cry (both of which use the "Life Regeneration" buff) used separately recover my character's HP up to 2933, but using Enduring Cry during the mastery's effect only goes up to 2341 HP. The UI reflects this, only showing a maximum of 1852 life per second, in both cases when Enduring Cry is used.

Switching the mastery with Surge of Vigour - "Every 4 seconds, Regenerate 15% of Life over one second", which does not use the "Life Regeneration" buff, in both cases recovers up to about 2500 HP. And this time the UI also goes up to 2462 life per second.

There are also the Guardian passive skill Time of Need and a Hunter influenced body armour mod which are worded similarly but which I did not test.

At the very least this is an unintuitive and inconsistent behaviour.

This is because Enduring Cry and the mastery provide regeneration through the same "Life Regeneration" buff. Buff/debuffs generally don't stack so when Enduring Cry is used, its buff overrides a weaker buff from the mastery.

I can't say for sure if this is by design or not. It probably makes sense for Lifesprig dual wielding to limit life regeneration on very low levels. But, as you noticed, many sources of "burst" life regeneration provide their effect directly, without involving the buff. So this implementation doesn't seem to be an informed decision for the balance sake or anything.