Once you start using a SensorPush WiFi Gateway in conjunction with your sensors, the monitoring pipeline moves mostly to the gateway and to the cloud, so this reduces what the app has to do by a lot. What happens is the Gateway relays the data of any in-range SensorPush sensors to the internet using your local WiFi or Ethernet, and the Gateway also monitors these sensor readings for alert conditions (to see if the readings have exceeded one of the boundaries you've set). If you have selected to receive alerts, then a push notification is sent via the cloud to your mobile device. All of that happens outside the app, and this is whether the app is onscreen or not.
So what happens is when you open the app, the app checks in with the sensorpush cloud to fetch updated data. It's kind of like an email app checking a server for new emails. There can be a few moments before it gets its update. This is likely the delay you are seeing before it updates. It's normal and okay.
Also like an email app, you can force the sensorpush app to check the cloud. To do this try a pull-down refresh (a.k.a. "swipe-down-to-refresh") on the main screen of the app. The main screen is the screen where the sensors are listed with the word "Devices" at the top. A pull-down refresh is the same thing you can do in an email app where you use a finger to pull down on the screen to check the server for new emails. This should load any new sensor and Gateway data from the cloud. The data that will come in from the cloud will be things like sensor readings, historical data, and gateway status.
Of course, if it doesn't update reach out to support and we'll definitely look into it asap!