All the Negative Buffs timer still ticking, but it will not deal any damage.
Depending on the situation, the Siren ultimate may even protect you and your team.
I've checked it last month, because a silly Siren kept using her ult to not die, and the Huskar on her team got mad because he could not attack us, and that fire DoT was dealing no damage while we were sleeping.
I've seem similar situations with :
- Silencer (his ultimate failed to silence everyone that was sleeping)
- Doom ultimate stopped dealing damage during the sleeping phase
- Pudge's Dismember got interrupted (yes, interrupted) as soon as siren used her ultimate