Hi @maxmorley,
What is the make and model number of the smart switch?
Post an image in your question of the wiring side of both switches showing how you've connected the wires.
Here's how on ifixit Adding images to an existing question
If the two original single switches were also side by side, they may have had a common power input i.e. only one power supply wire connected to one switch and then a smaller wire (or internal busbar if dual switch box) connecting from that wire over to the 2nd switch input side i.e. the power supply was connected in parallel to both switches.
The output side of each switch would have their own wire feeding to the particular circuit that they controlled
crwdns2934105:0crwdne2934105:0
crwdns2934113:0crwdne2934113:0
crwdns2915270:0crwdne2915270:0
crwdns2889612:0crwdne2889612:0
1