When changing any switch like for like, the wires should be connected in the same configuration in the new switch as they were in the original switch. Failure to do this means the lights will not work as they did.
The new switch will not work as it should because you have wired in incorrectly.
Look at it this way. The old switch with the old wiring worked. The new switch with the old wiring does not work, it only does not work because you have wired it wrong, you have proved that by saying one light does not switch off, so since the wiring is the same as it was, the switch is brand new, it must be wired wrong.
If it helps, your new switch is the same as the old switch, but it is two switches, one is upside down in relation to the other, a lot of folk get it wrong because of this.
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