It looks like you're just squeaking by on the big-big combo. If it shifts into and out of that combo without a lot of crunchy sounds then you just made it on the safe side and can use the Tiagra without any issue. Even if it makes light crunchy sounds but shifts into and out without the chain getting really tight (check it for up and down play while the chain is crossing teeth at either end) it'll be OK since it's not actually going hard tight to the point of jamming. If it DOES go guitar string tight and you can feel definite harder resistance as it crosses into and out of the engagement then you're straining the chain and components and should consider a switch or just be extra careful to avoid the big-big combo.

As for the lack of tension on the small-small combo who cares? You'll never (shouldn't) ride in that combo anyway. And technically you should never be in the big-big combo either but as Bill says accidents happen and it's nice to know it won't bust a button if you select that combo in a moment of non thinking.

Outside of that just stay attentive so you don't cross chain and it'll work marvelously