That is not correct. The Act says no such thing.
If the convicting court decided that an absolute discharge was an appropriate sentence, that would be immediately spent, but these are not often seen.
Whilst a conviction for a railway byelaw offence will not ordinarily appear on a DBS check, this is by virtue of the fact it is not an imprisonable offence or otherwise specified in regulations as a recordable offence, not because it is "immediately spent".
This is not right either. A lot of employers would say they have "a specific need to know" about all convictions, but the only ones entitled to know about spent convictions are those recruiting a role specified in the various regulations as entitling them to ask.
In practice, someone with a recent conviction for a railway byelaw offence who does not declare it is unlikely to find their employer discovers it, because it is non-recordable, but...
This I agree with.
It is important that you follow your own advice