Sorry, I can't report this ever happening to me. It's likely happened in my 30 years of using pumps but it was rare. As others have reported, I've found myself with post-set-change highs, especially with the Omnipod.
What you're reporting could be explained by significant changes in insulin sensitivity at the site. It's fairly common among pumpers to experience third highs with a site. Absorption becomes impeded and degrades your insulin sensitivity.
One way to explain your first day lows is that a fresh site is super sensitive to insulin and will produce lows unless you adapt and change your pump insulin sensitivity (for corrections), insulin to carb ratios (for meals), and basal rates. It may be possible to create a "bundle" of settings on your Omnipod that you could invoke for your first day sites only. You could arrive at these settings by experimenting with manually making these changes.
If I were you I would experiment with these settings and document what you're doing as there are enough variables in this equation to lose track of what's really going on. Writing stuff down will help you really learn what is happening.
When talking, writing, and thinking about these settings, keep in mind the inverse relationship embedded in them. Increasing a 1:40 insulin sensitivity means decreasing the number to say, 1:30. For an insulin to carb ratio increasing from 1:10 to 1:15 (unit of insulin : grams of carbs) is actually decreasing the amount of insulin delivered. (I apologize if I've just explained this math concept to a PhD in mathematics!) For me, I find it's easier to think in terms of becoming more or less aggressive with the insulin.
Good luck! I think this is a solvable problem. Please report back what you discover. While I don't think your experience is common, putting it in the record here may very well help someone later.