If the input data is correct and there aren't any calculation errors, then the discount curve should be decreasing (just like your second chart).
Using a no-arbitrage argument, Hagan & West (2007) state:
As already mentioned, the discount factor curve must be monotonically
decreasing whether the yield curve is normal, mixed or inverted.
Nevertheless, many bootstrapping and interpolation algorithms for
constructing yield curves miss this absolutely fundamental point.
This should be straight forward to see for a zero coupon bond $Z$ (assuming continuous compounding):
$$Z(0,t)=exp(-r(t)t) \ \Longleftrightarrow \ r(t)=-\frac{1}{t} ln Z(0,t)$$
Naturally, if you just randomly bump a zero coupon rate and recalculate the discount factors you will get a spike like in your first chart. That's why you should bump the traded instruments, then re-strip the curve and re-calculate your discount factors.

So to answer your question: my guess is that chart 1 doesn't show a consistent discount factor curve and there's either a calculation error or the rates $r(t)$ have been bumped like in the above example.