I can't see the white spots you refer to. Overall, the plant looks fine.

That said, I suspect the white tube is for irrigation?
Is it to apply the water?
Or to remove excess from a container without a drain hole?

Attached is another photo with better light and the white spots circled

(https://imageshack.us/a/img703/6018/whitespots.jpg)

Aside from the white tips the plant looks healthy, but if it's some sort of infection I wanted to catch it before it spreads.

The tube is for watering - the tomato is in a DIY self watering container.

That's normal fluid leaving the leaves because of high soil moisture and/or high humidity. Called guttation.