Most likely normal, but it matters which phrase they used. Additional interest only means your insurer notifies the landlord if the policy is cancelled, lapses, or changes. It does not give the landlord coverage under your policy and generally does not let them file a claim. Additional insured is the one to be cautious about, especially if they want it on the liability section; it can potentially pull your policy into building-wide claims or make you cover defense costs in ways you didn’t intend.
In a prewar multi-family, management companies often standardize this after a fire or water loss where a tenant’s policy had lapsed. They want proof they won’t be chasing an uninsured tenant, and they want renewal reminders if you drop it.
Before signing, ask your carrier for an endorsement naming the management entity exactly as it appears on the lease as additional interest. It should cost nothing, or close to it. Keep the liability limit at something reasonable for your stuff and risk. Don’t let them list themselves as additional insured unless the lease says why, and even then push back if it’s broad.
The bigger red flag would be if the rider requires a specific carrier or a minimum personal property amount that’s wildly above your actual stuff. That’s not typical and could be someone selling insurance or trying to force you out. In your shoes, I’d sign only after the endorsement and a copy to the management office, not before.
