It is possible for all the users to have their own respective 'TPCloud Company' or if all tokens are associated with a single email/account. Below is a detailed procedure on how to achieve this:
Firstly, when people are invited to TPCloud from an existing TPCloud Company, that do NOT have an existing TPCloud account, they automatically become an associate of the inviting users TPCloud account (as in your case you are an Admin but do not currently have your own 'TPCloud Company'). As such, these accounts see all tokens associated with the inviting account (Andy's), as well as any tokens of their own (assigned to their own email). Although there is a button to share tokens in those accounts, this has nil effect as without a 'TPCloud Company' you have no "Invited members".
So, when you want all users to be able to share their own tokens with others all individuals need to create their own TPCloud company (by clicking the 'top-right-of-TPCloud-email-address > My Company > Create Company'). At that point, they will need to invite any people they want to share with to their TPCloud, as well as make their tokens Public.
After creation of your own TPCloud Company, to manage and maintain tokens between "Companies", you can select via a drop-down company list underneath the "TPCloud BETA' logo (top-left of the website), available when you are a member of more than one company.
Sometimes, businesses prefer using a single account for access (e.g. 'firstname.lastname@example.org', managing the password/access accordingly for their users. You can still do this without everyone migrating to individual companies provided people use the 'Move Token' option available in 'TPCloud > Tokens > (token) > View Details' within their current accounts to move tokens to the "parent" TPCloud Company, and once that is made Public will be shared with all members of the company.
Note: If you plan to share only the tokens with other companies under your TPCloud profile, all the labels associated with your account, by default, are also shared. The labels are listed below the token lists on the bottom left pane within your TPCloud account homepage. It is not possible to only share the tokens without sharing the labels with other companies.