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Merchant sets their price in dollars (for example) and the price in Bitcoin is calculated when a transaction is made using the current btc exchange rate.

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Stripe (in this case) receives bitcoins and it is exposed to fluctuations. So, if Stripe guarantees the seller a price for the bitcoin, I would think that Stripe has a mechanism to limit or even eliminate the risk from that exposure. I am interested in learning how Stripe does it. Do you know how Stripe does it?

Can they do the conversion realtime and charge the client whatever rate they get?

Perhaps, but they don't say it explicitly. For example, Bitpay says (at https://bitpay.com/)

` Charge $1, get $1 Instant conversion, no transaction fee, and bank deposits in US Dollars, Euros, GBP, CAD and more. We take the bitcoin exchange rate risk, your customers get the best rate on the market, and you get a payment you can count on, every time. `

Maybe they just hope that the fluctuations will balance out?

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