Install the pricing extensions by going in: Settings > Configuration > Connector and by checking the Price are managed in Odoo with pricelists option.
Verify that the option Use pricelists to adapt your price per customers is active in the Odoo Settings > Configuration > Sales.
The pricelist used for the prices sent to Magento is configured on the Magento Backend (Connectors > Magento > Backends). Magento will use theses prices as default prices.
In Magento, the default is to share the prices between websites. If you want to have different prices per websites, go to System > Catalog > Catalog > Price and set the Catalog Price Scope to Website instead of Global.
When you need different prices for a website, set the pricelist for this website in Connectors > Magento > Websites.
The prices are actually updated on Magento when the price is changed on the products, not when a pricelist is modified.