The Wifi outlet seems like mega overkill to run a schedule. Couldn't you just use one of these? https://www.google.co.uk/search?q=socket+timer+us&safe=off&b...
This wouldn't work if you want 1 minute a week (since the cycle repeats every 35 minutes), but for hydroponics sometimes you want a short duration with very frequent repetitions, and the electronic timers (which are preferable in most other ways) don't provide enough on/off cycles per day or week.
You would plug in timer 1, so that its output (output 1) is on. You would set timer 2 so that output 2 would turn on as soon as timer 2 receives power. When there are only 30 seconds left in timer 1's on cycle, you would plug timer 2 into a separate outlet.
Since they are synced, but only overlap by 30 seconds, they will only both be on for 30 seconds. You would then need some kind of AND that would only turn on the pump if output 2 and output 1 are both on.
You'd need to separate the timer power from the switched power. Easy to do, but not how the cheap ones work.
Also, the settings are not precise enough to get a repeatable interval across two devices.
On the other hand, it's a very simple DIY electronics project. Arduino is extreme overkill, but will also work.
The IoT future is looking very bleak, with all the vulnerabilities it's going to introduce.
"A Word on WiFi Sockets: They suck. They take the simplest operation of closing a circuit and abstract it in a shitty smartphone app that only works half the time."
Short interval timers are a bit harder to come by, as several others have mentioned, but they do exist and aren't very expensive. E.g. this one can go as short as one minute per week:
http://plumbdeal.com/product_info.php/grasslin-digital-plugi...