When I am discussing previous work, according to APA formatting, it is clear I should use past "Alicke (2000) described....". However, what tense do I use to explain their results? Aka "The model postulated..." vs. "The model postulates..." where "the model" is part of Alicke's findings. Past or present?
While the past tense is perfectly sensible for discussing published work (which was necessarily undertaken and published in the past) it is also acceptable to discuss these in the present tense -- e.g., "Alicke (2000) models the conditions that cultivate or mitigate blame". In academic work it is legitimate to treat each cited paper as if it were akin to a person who is here with us making an argument, so that the academic literature is like a dinner party, with argumentative guests.
In view of this, it is acceptable to talk about a paper in the present tense, even if it is very old. You can make it sound like Aristotle is right here with us, arguing with Kant. You can even make it sound like papers by the same author are independent dinner-party guests, arguing against each other -- e.g., "Johnson (2010) argues that capitalist production methods were a net benefit to rural economies, notwithstanding outward migration of workers to cities; Johnson (2011) demurs on this issue, and Johnson (2013) seems to completely disagree".
Some things to note:
APA style allows either past or present tense for discussing the literature, so long as you are consistent.
Style guides are all well and good, but they have sometimes been described as "anti-style" guides. Excessive adherence to their conventions can have the negative effect of sucking the style out of your writing. (In fairness, this is something that the style guides themselves acknowledge, in their discussions of smoothness of expressions.) What is more important than strict adherence to style guides is consistency, clarity, smoothness and readability of your writing. Make your writing clear to your reader, pleasurable to read, and be consistent in your use of tense.
When considering appropriate tense, be sure to correctly identify the subject of each sentence. In the example you give in your post, the subject of the latter sentence is "the model", not the original paper or its author. Since a model is an eternally lasting description of reality, it is standard to speak of what the model does in the present tense, even if you are referring to the paper that introduced it in the past tense.
There is often some freedom to maneuver, but make sure you are consistent with tense for subjects of the same type. So if you say "The model postulates..." in one place, don't say "The model predicted..." in another place. If you start talking about another model, treat it using the same tense convention. If you start talking about another type of subject (e.g., a paper, or an author) you may use a different tense if it is still clear and readable.