We start by numbering the cables in your diagram from left to right:
- is an always-hot feed backstabbed into the single pole switch (it's always hot because it's backstabbed at the same end of the switch as the incoming hot feed).
- is another always-hot feed (were I to guess, this is the circuit coming in, but there's an off chance some dunderhead wired it to come in on cable #1 instead). I can tell because of how it's double-looped at the switch terminal screw then pigtailed off to the rest of the switches.
- is the outbound switched hot from the single pole switch to whatever lighting is on it. (It is connected to the other end of the switch from the hot terminal.)
- is the outbound dimmed hot to its corresponding lighting load.
- and 6. are the curious cases -- you'd expect both travelers to be in 6. but perhaps the two cables are run together as part of the same circuit in a California 3-way configuration? (The traveler terminals on a 3-way switch are both at the same end.) Either way, they're irrelevant to your timer trouble.
From here, we can tell where your error is -- you wired the switched hot on the timer to cable #1's hot, when the original single pole switch was switching cable #3's hot.
So, turn off the power to the circuit, then unnut the hot (black) and switched (red) wires on the timer, and unwind the switched wire from cable #1's hot and cable #3's hot from the pigtail junction. Then use new wirenuts to nut cable #1's hot into the pigtail junction and cable #3's hot to the switched wire from the timer. Put everything back together, turn it back on, and enjoy your new timer!