A “turn” for Tiamat encompasses the actions of all of her heads.
Tiamat’s description reads:
On each of her turns, she uses one or two breath weapons, trying to
exhaust all of them so she can unleash her chromatic breath.
(Draconomicon, Chromatic Dragons, Tiamat, page 245.)
“Each turn” for Tiamat encompasses the actions of all her heads. (If each head got its own turn, then there would be no way to use two breath weapons on a given turn, as stated above.)
Her turn would begin on initiative count 45.
Also, Tiamat’s Frightful Majesty power ends on “Tiamat’s next turn” also indicating that it is Tiamat that gets a turn, not her heads.
The 6 Stat Blocks
There are 6 stat blocks for Tiamat: one for her and one for each of her heads. Only the “Tiamat” stat block lists Hit Points, so damage is dealt to Tiamat not to any particular head. So Tiamat’s Hit Points are reduced at the end of Tiamat’s turn.
The “White Dragon Head Only” stat block mentions “the end of this head’s next turn.”
We are left with a bit of a muddle: Tiamat has one turn a round, but each of her heads do as well.
But while a head can be said to have a turn, it has no Hit Point statistic to affect. Ongoing damage to Tiamat should occur on “Tiamat’s turn” — not the turns of her heads.
Contrast to the Ettin stat block
In contrast to Tiamat, an ettin (either Marauder or Spirit Talker) explicitly “gets two turns during a round, and has a full set of actions (standard, move, minor) on each turn. Each set of actions corresponds to a different head.” (Monster Manual, p.108).
While the ettin explicitly gets multiple turns per round, Tiamat explicitly gets a singular (albeit, multi-part) turn. Both of the ettin’s head gets a “turn” while each of Tiamat’s heads are called an “activation.”
The ettin’s ability to take immediate actions refreshes on each of its
(MM, p 108)
Tiamat’s ability to take immediate actions refreshes on each head’s
(Draconomicon, Chromatic Dragons, p. 245)