I don't remember exactly but I think the timers are 2/4/6 hours for the actions. In my experience you really need to be on time for your plants to level up. If you leave your plants for too long (actions are stacking) they might downgrade and it will take even longer. For example, if you just planted then level 1 to level 2 will take 2 hours (when the water shows up). But if you're late and water+dust shows up then you have to water and dust them all and then wait for the next action, then they will grow.
Make sure your friends kill the spider webs and worms as they will downgrade your plants too.
Like Shae said checking your buddy garden every hour is probably the easiest thing to do.
The bug used to exist but I told support and it was fixed around August 2017. The bug then came back with the 12th April 2018 patch and has not been fixed since despite having contacted support several times.
If you are wearing the Great Job! Stamp hat and have DJ, there is a chance for a bonus mission to appear -
But instead it is currently bugged and you will disconnect if the bonus mission appears.