You could use _mm256_store_pd( (double*)t, a). I'm pretty sure this is strict-aliasing safe because you're not directly dereferencing the pointer after casting it. The _mm256_store_pd intrinsic wraps the store with any necessary may-alias stuff.
(With AVX512, Intel switched to using void* for the load/store intrinsics instead of float*, double*, or __m512i*, to remove the need for these clunky casts and make it more clear that intrinsics can alias anything.)
The other option is to _mm256_castpd_si256 to reinterpret the bits of your __m256d as a __m256i:
alignas(32) uint64_t t[4];
_mm256_store_si256( (__m256i*)t, _mm256_castpd_si256(a));
If you read from t[] right away, your compiler might optimize away the store/reload and just shuffle or pextrq rax, xmm0, 1 to extract FP bit patterns directly into integer registers. You could write this manually with intrinsics. Store/reload is not bad, though, especially if you want more than 1 of the double bit-patterns as scalar integers.
You could instead use union m256_elements { uint64_t u64[4]; __m256d vecd; };, but there's no guarantee that will compile efficiently.
This cast compiles to zero asm instructions, i.e. it's just a type-pun to keep the C compiler happy.
If you wanted to actually round packed double to the nearest signed or unsigned 64-bit integer and have the result in 2's complement or unsigned binary instead of IEEE754 binary64, you need AVX512F _mm256/512_cvtpd_epi64 (vcvtpd2qq) for it to be efficient. SSE2 + x86-64 can do it for scalar, or you can use some packed FP hacks for numbers in the [0..2^52] range: How to efficiently perform double/int64 conversions with SSE/AVX?.
BTW, storeu doesn't require an aligned destination, but store does. If the destination is a local, you should normally align it instead of using an unaligned store, at least if the store happens in a loop, or if this function can inline into a larger function.