Well, the Rho Aias projected by Archer is a conceptual weapon/armour. This means that it is not necessarily THE shield wielded by Ajax, but it fully embodies the concept of "absolute defence against projectiles". As a result, Archer could have come across it without time travel.
Now a POTENTIAL scenario could be as follows:
Archer came across a shard of the original Rho Aias during his life time. Because of his ability to analyze the composition, and most importantly, the history and concepts carried by an item, he was able to extract the Noble Phantasm (in this case, an idea) and wield it. The scenario could be somewhat similar to how Shirou extracted Nine Lives from a mere stone slab. Also, backwards time travel is highly unlikely, since as far as we know, time travel, particularly backward time travel, is still considered a True Magic.
Also, the originals in the Throne of Heroes are not altered after induction. So even if Archer has seen Rho Aias as a servant, he will not be able to use it the second time around. Archer must have come across Rho Aias when he was alive.
Are we Beast's Lair Lite? Are we?!