Wiring a dimmer and timer side by side
It appears like you wired your neutral wire on the leviton switch to your hot or load wire in the box. The white wire on the leviton switch is a neutral. 

Smart light switches like leviton switches require a neutral wire to operate to provide power to the timer chip constantly. The white wire on the switch should be wired to the white neutral wire in the box. Non smart light switches didn't require a neutral that's why they are just tied together in the back of the box. 

Connecting the hot or load wire to the neutral wire as you have done with light switch on the right can be dangerous as that is not how the switch is designed to operate. If you're uncertain of the wiring it's probably not a bad idea to get an electrician or a friend that's familiar with electrical to help you out. That being said you can fix the issue. 

I would recommend replacing both of your switches with Lutron Caseta switches which would allow you dimming control, allow you to remotely set a schedule or timer from your phone and would be less confusing to install.  

Without an existing picture of how the orginal light switches were wired it's hard to diagnose which wire is the hot and which one is your load wire (the one that goes to the light fixture) 

The advantage of the lutron caseta light switches is that they don't require a neutral wire and they wire up just like your old switches and if you wire the hot and load wire backwards it won't matter. Which makes them easier to install. 

So on the left you would wire the new lutron switch with the red wire and black wire. On the right you would wire the two black wires to the new switch. And both new light switches should have their grounds properly terminated which it looks like you have done in the original installation. 

I found this smart light switch installation guide: helpful with videos that show you how to install the lutron caseta style light switches with no neutral. 

Disclaimer: I don't work for lutron but in this situation I think it's good solution for a DIY fix to the current wiring situation with the information provided. See comments below for more details.