Is earning money from the NeoBux website as a free member, then upgrading the membership with the earned money instead of withdrawing it, considered unlawful?

There is no harm in earning money from browsing advertisements on the internet, provided certain conditions are met: that the subscription is free, that the advertisements are permissible (halal), and that the compensation is known. There is no difference between paying money to upgrade membership from your own personal funds or from what you have earned from the website.