All distance vector routing protocols advertide the entire routing table to the neighbor.
In case of RIP, once the route is received from the neighbor, the router checks its own router table and increments the hop count if necessary. This is performed everytime an update is received.
An eg will help you understand this better.
R2 send the route information 172.168.10.64/27 to R1 with hop of 0. R1 adds one hop to it and will advertise to any downstream routers which will add 1 to the advertise metric thus making the hop count as 2.
In the above case due to split horizon the update sent by R2 will be received by R1 and will update its own routing table.Similar is the case for the networks adv br R1 to R2. This process repeats every update cycle.
so the route adv with a metric of 1 in the first update will still be adv as metric 1 to the second router after the update interval.
HTH, rate if it does
Narayan