Basically Snapseed interprets your iPhone's color profiles more aggressively than Lightroom does, so what you're seeing is real but exaggerated by the app, not by iOS. When I edit photos on my phone and switch between apps I notice exactly the same thing - in Snapseed everything looks more vibrant and saturated, while in Lightroom the tones stay closer to what I see on screen.
What works for me is making adjustments in Snapseed but then pulling down the overall saturation a bit before saving, or just going into the "Selective" tool (the finger one) and desaturating only where it looks too strong, especially in skin tones where the color boost is most noticeable.