1AR: "Neg asked how we got the numbers for X, Y, and Z. My partner and I researched that information on the internet and compiled a table of figures for A-Z. Our figures come from government websites and are displayed on that table."
2NR: "The numbers for X, Y, and Z are misleading for three reasons. [reasons] Furthermore, the numbers they claim are good are actually bad because of [reasons]. Finally, X, Y, and Z are insufficient proof for the general trend claimed by the negative team."
2AR: "I encourage you to look at our table after the round and view the statistics for A-Z and see that X, Y, and Z are just an example of the benefits of all of such figures in existence."
First-time community judge: "Yes, may I see your table of figures?" *reads table and is influenced by information never presented in the debate*
How should neg proceed? Is there a right way to prevent that?
It appears you are misrepresenting what happened unless your claim is the table they gave the judge is not the table they were attesting to in the round.
Everything that happened seems 100% appropriate.
AFF : Makes an assertion
NEG: Questions how the assertion was arrived at
AFF: States it was compiled various government websites and are displayed on this table
NEG Claims the numbers are misleading and not sufficient proof
AFF: Claims numbers are a valid explanation of the aff benefit and judge is free to examine them after the round.
JUDGE: Let me see the table
This to me seems absolutely what you would expect from a debate round.
Your only ground for protest would be if the table said something different than what the aff attested to which could be cause for removal from the tournament or unless you believe the table was fabricated in some kind of way.