These transceivers speak standard 10BASE-T on the network end (I'm using the very same model with an A2060 NIC) - they're compatible with any common 10/100/1000 twisted-pair port.
You might want to make sure though that the legacy NIC supports proper auto negotiation - not all legacy equipment does. Depending on the exact hardware, leaving the switch port in auto-negotiation mode might (in rare cases) produce a duplex mismatch that would cause all communication to really crawl.
Ideally, check the switch port's duplex mode when it comes up, generate some serious traffic and watch for excessive collisions and late collisions (for half-duplex mode), or FCS error and runts (for full-duplex mode). If the NIC can throughput multiple Mbit/s you can rule out a duplex mismatch.