to fill something up: to put contents into a container or space until it will hold no more
This is the ordinary Greek verb for filling a container, and what goes into the container is always something you could see or touch: water in stone jars, sour wine in a sponge, burning coals in a censer, leftover bread in baskets. The word never reaches for anything grander, which is why it belongs to scenes of ordinary work rather than to the New Testament's language about people being filled with the Spirit.
Its close relative γέμω reports the finished state, that a thing is full. This verb reports the event that gets it there. It usually names both the container and what is going into it, and it puts the reader in the moment when the level is rising.
When no one is said to be doing the filling, the sentence simply watches a space reach capacity: the storm driving waves into the boat in Mark 4:37, the master sending his servant out to the roads until the house is full in Luke 14:23, smoke pouring into the heavenly temple in Revelation 15:8. What matters in those verses is not the hand doing the work but that the container is being brought to its limit.