It's not bit swapped, the high byte is in a different place but the bits of each byte are still in the same order.
03 E8 vs. E8 03
You do have to be aware of the size of the data though. Reading/writing a sequence of bytes vs a sequence of words for example.
A sequence of byte data could be 03 E8 03 E8 and would not need swapping, you're reading each in order.
A sequence of word data would still be 03 E8 03 E8 but you need to know to swap based on the intended size so that it correctly reads as E8 03 E8 03.
Loading a register should swap on the read, so A0 would already point to the right location. Once the data is in a register it's already swapped as needed based on the instruction used to read it. Transfer between registers wouldn't need a byte swap.