The models under the two parameterizations are equivalent models, meaning they have the same log likelihood (-2LogL for Intercept and Covariates) and the same predicted values for any setting of the predictors. Because continuous exposure2 is involved in interaction with CLASS exposure1, its parameter has to change because the parameters for exposure1 and exposure1*exposure2 must change due to the change in reference (and therefore interpretation as Rick mentioned) in order for the predicted values to stay the same. But as in all models of whatever type, when a variable is involved in an interaction with another variable, its effect can only be interpreted at each level of the interacting variable. So, the p-value for exposure2 is really not relevant given that it interacts with exposure1. But to clarify the reason for the change, the interpretation of the exposure2 parameter is the effect of a unit increase in exposure2 at the reference level of the CLASS variables. And the effect of exposure2 at the level might be different and might or might not be significantly different from zero. Either parameterization is fine, you just have to be sure any statement of the results are consistent with the interpretation imposed by the parameterization that is used.
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