Yes. Indian passport holders need a pre-arranged UAE visa before flying to Dubai. Tourist visas are typically arranged through airlines, hotels, or travel agencies, and the process takes a few working days.
One exception: Indians holding a valid US, UK, or EU visa or residence permit can get a visa on arrival in the UAE.
Compare that with Americans, who get a free 30-day visa on arrival in Dubai with no advance paperwork. Same airport, completely different rulebook, decided entirely by passport.

For families, apply together through one channel so everyone's visas arrive on the same timeline. Split applications across different agents is how one family member ends up cleared and another does not.
Sources: U.S. State Department, IATA Travel Centre
Dubai visas for Americans are visa-on-arrival; the prep is knowing the entry rules, not filing paperwork.
PassportPower handles family and group UAE applications as one batch for $9.99 one-time per destination, so nobody's paperwork lands on a different schedule.