If it requires you to have an account on another site to complete the product review project that you have, that is okay. Please note that your contract and all payments should be done through Upwork. Let us know if you have other questions or need assistance with, thank you.
re: "I got my first job (product review) but they require that I register using their site."
Lots of jobs will require you to register on another site in order to do the work.
In fact, lots of the jobs that I do personally require me to register on another site. I do database design and programming work, and I often need to create an account on a client's site in order to work on their source code or test my work. There is nothing wrong with that.
Standard caution: Use a unique username and password when you do this.
It would be very rare to encounter somebody up to no good who is trying to harvest your username and password from such a registration and then use it to hack into your other sites. But that is technically possible. So you don't want to re-use a password while registering.
Also: Upwork has no specific prohibition against writing product reviews. For example, if I am a client and I create a website about toothpase, I could hire you to write a review about a new Colgate toothpaste product, so that I could post that review on my website. That would be fine.
BUT: Upwork ToS specifically prohibits freelancers from violating other sites ToS, and Upwork strives to be a "good neighbor" to Amazon.com by supporting their prohibitions against paid reviews. Amazon.com has some very strict rules against paid reviews. Amazon.com WILL go after people who violate their rules against writing reviews for pay. And Upwork policy is to not allow jobs which violate these rules.
If a client owns a website and is asking you to register an account on their own website, then obviously they themselves can decide what their own website's rules are. So if you are being hired to write product reviews that appear on their own website, that would be fine.