No, this is not required by Attribute Based Encryption (ABE), however it is a common practice to use so-called "hybrid encryption" when you want to encrypt data using public-key encryption, for multiple reasons:
- it sometimes avoids the need for padding of the message: if your ABE scheme works on messages that are of size 256 bits, for instance, then using a AES key of 256 bits fits naturally in that message space. (Although in practice you often have some rejection sampling to do because the whole 256-bit space is not necessarily the universe of the messages.)
- it allows to ignore the limits of the public-key encryption scheme you are using, that is the converse of the previous point: if you can only work with 256 bits messages but want to encrypt more than 256 bits, then you have a problem, whereas AES (with a good mode of operation) (or the underlying stream cipher of your choice) is not limited in the size of the data you can encrypt.
- probably one of the most important reasons: the performance! ABE (and more generally public-key cryptography) schemes are super slow in practice, while AES is super fast, so in order to have decent performance it makes sense to use as little public-key cryptography as possible.