Is this behavior of the Series function correct

While series expanding a function, I got an unexpected result, which seems like an error to me. I have boiled it down to this minimum (non) working example:

$  Assumptions = p \[Element] Reals && x \[Element] Reals; k = Conjugate[(x^2*(1 + I *p))^2 - x^2*(1 + I*p)]; Expand[FullSimplify[Series[k, {x, 0, 2}]]] Series[FullSimplify[k], {x, 0, 2}] // TraditionalForm 

This returns

-x^2 + I p x^2 + x^4 - 2 I p x^4 - p^2 x^4 

and

I (p+I) x^2+O(x^3) 

The second output, where I have first used FullSimplify returns the correct output. To my understanding, the first output is wrong. Have I found a bug, or is there something about the Series function I don’t understand.