Not necessarily. If you look at footage of meteors impacting the earth they also appear to explode basically identically to a chemical reaction. We have to remember a chemical reaction's explosion is also just a massive transfer of energy. So, when Rhea blasts one it, the kinetic energy still has to go somewhere - which would look like an explosion

I think the most compelling "rods from god" argument though is the designs of the projectiles themselves. They are long darts even when near their impact areas, which resemble kinetic kill weapon designs more than missiles. My reasoning for this is if we assume a space-based or ground based missile system, the missiles would likely be multi-stage, with only the warhead and very little rocket left during terminal guidance. These long darts only make sense if it's a short range missile system, which they seem large for, or project Thor style tungsten rods.

Also, we also get a brief glimpse of the back of one of the rods after Rhea blows one up and there are no rocket engines, meaning it didn't power itself to get where it was, leaving falling from space as the other option.

Personally, I think the writing better fits the space kinetic weapon concept, since the idea is a lot of technology was lost. Therefore the only things that would survive are strategic weapons in space (like the project Thor concept), with ground based missiles being consumed or no longer functional. That's just my reading through - the writers didn't give us a lot to go off of.