What does fusion of powers mean ? It means that one branch of government, or the members of one branch of government, have also automatically the power to directly influence another branch of government. For instance the government must gain a vote of confidence from the assembly, the assembly may grant to the government the power to make delegated legislation or the head of government is automatically a member of the assembly.
I think that the lecturer was saying that members of the assembly are not automatically members of the executive or viceversa. The ones that are both members of the assembly and the government are chosen by independent authorities, for example they are nominated by the head of government and elected by the citizens. So, when they work as members of government it's because they were chosen by the head of government, while when they work as members of the assembly it's because they were chosen by the people. That is to say, members of the government are not necessarily members of the assembly, if they are, it's not because of any law.
Of course they may be countries in which a member of the assembly is by law a member of the government, in such ipotetical situations there would be fusion of powers.
On the other hand, the textbook was saying that the [head of] government may be forced to gain a vote of confidence by the assembly and this is indeed an example of fusion of powers, because the government depend necessarily on the assembly. It can't be elected by the people.
So I think that both were right. Fusion of powers does not happens if one person happens to hold executive and legislative power, it happens if one person hold executive and legislative power automatically because the law estabilished that. Of course historically there have been cases of offices that were held together by convention that became held together by law.