Did electrician connect this service entrance box wrong?
Yes.  The panel's labeling means exactly what you think it means, that breaker slot 5-6 and all above it are limited to 70A breakers max.  That 100A breaker should be moved down to the bottom slot.  

Additionally, that top breaker is being backfed by your solar setup, correct?  In that case, it needs to be bolted down -- that's a code requirement whenever a breaker is backfed.  You'll need a HOM4RK2HA bolt-down kit, which you (or your installer) will probably have to get from a proper electrical supply house.