If a probe is pushed by solar system rotation into a space with multiple bonuses (such as a comet and a publicity icon), the player receives all applicable bonuses.

• On page 9, it states: "If you move into a space with a publicity icon, gain 1 publicity. (There is no publicity for visiting Earth.)"
• The FAQ on page 28 clarifies: "Will I get [publicity] if the solar system pushes my probe onto a space with a comet? Yes. Your probes will always give you [publicity] when they visit a space object, even if it isn't your turn."

The rulebook does not specify a required order for resolving multiple bonuses when entering a space. Therefore, you receive all bonuses, and the order is not specified or restricted.

Source: pages 9 and 28.

Source: Core Rulebook (pp. 10, 17, 28, 8, 9)