for those who want to know about who's impacted :

"Intel. We notified Intel about our findings, including a preliminary writeup and proof-of-concept code, on January 31st, 2019. Intel had acknowledged the issue and requested an embargo on the results in this paper, ending May 14th, 2019. Intel has further classified this issue as Microarchitectural Store Buffer Data Sampling (MSBDS), assigning it CVE-2018-12126 and a CVSS ranking of Medium. Finally, Intel had indicated that we are the first academic group to report this issue and that a similar issue was found internally as well.

AMD. We also notified AMD’s security response team
regarding our findings, including our writeup. AMD had investigated this issue of their architectures and indicated that
AMD CPUs are not vulnerable to the attacks described in this
paper.

ARM. We have also notified ARM’s security response
team regarding our findings. ARM had investigated this issue
and found that ARM CPUs are not vulnerable to the attacks
described in this paper.
IBM. Finally, we also notified IBM security about the
finding reported in this work. IBM had responded that none
of their CPUs is affected, including System-V and PowerPC."

And here's a description (from the paper) of the mechanisms :

"The Mechanism Behind Fallout. Fallout exploits an optimization that we call Write Transient Forwarding (WTF),
which incorrectly passes values from memory writes to subsequent memory reads. In a nutshell, when the program writes
a value to memory, the processor needs to first translate the
virtual address of the destination to a physical address and
then acquire exclusive access to the location. Rather than
stalling the store instruction and subsequent computation, the
processor records the value and the address in the store buffer,
and continues executing the program. The store buffer then resolves the address, acquires the access to the memory location
and stores the data.

When a value is in the store buffer, care should be taken
that subsequent loads from the same address do not read stale
values from memory. To solve this, the processor matches
the addresses of all load instructions against addresses in the
store buffer. In the case of a match, the processor forwards the
matching value from the store buffer to the load instruction. To
increase efficiency, the processor uses partial address matches
to rule out the need for store-to-load forwarding. WTF kicks
in when a load instruction partially matches a preceding store
and the processor determines that the load is bound to fail. In
such cases, instead of cleaning up the state of the processor,
it marks the load as faulty, and incorrectly forwards the value
of the partially matched store.

Exploiting the WTF optimization. Fallout exploits this behavior to leak, through a microarchitectural channel, the value
that WTF incorrectly forwards. The attacker deliberately performs a faulty load, causing the CPU to transiently forward
an incorrect value from the store buffer. We subsequently leak
the value using a Flush+Reload [58] side channel. As the store
buffer is a shared resource used by all software running on a
CPU core, the incorrectly-forwarded value might not even belong to the attacker’s process."