What is the ruling on one who raises his head from prostration thinking that the imam has said the takbir, then returns to his prostration?

Al-Hawini: Our brothers in the neighboring camp were praying the 'Asr prayer with us. They were in prostration when they heard your takbir here, so they raised their heads. Then they saw that the imam was in prostration, so they prostrated again. What is the ruling on their prayer? I mean, they thought the takbir was from their imam, so they raised their heads, but they found the imam in prostration, while the takbir was here.

The Shaykh : I mean, they thought there was an imam for them other than the imam who is here.
Al-Hawini: No... I mean, they were in prostration, then they heard the takbir here, so they thought their imam had said the takbir to raise their heads from prostration. They raised their heads, only to find the imam in prostration.

The Shaykh : Their specific imam.
Al-Hawini: Their specific imam.

The Shaykh : I mean, they heard our takbir here, so they thought it was the takbir of their imam.
Al-Hawini: Yes. Yes.

The Shaykh : Well, when they heard the takbir from here, they thought it was the takbir of their imam, so they raised their heads. Then they realized the situation and joined the imam in prostration. So, they owe nothing.
Al-Hawini: They owe nothing.

The Shaykh : They owe nothing.