The danger of relying on dictionary definitions is 1) they frequently do not reflect contemporary or colloquial usage and 2) you can find one to support almost any interpretation.
FWIW, American Heritage Dictionary lists the following definitions for “secularism.”
1. Religious skepticism or indifference.
2. The view that religious considerations should be excluded from civil affairs or public education.
And the following is fromt eh Wikipedia article on secularism:
“In one sense, secularism may assert the right to be free from religious rule and teachings, and freedom from the government imposition of religion upon the people, within a state that is neutral on matters of belief, and gives no state privileges or subsidies to religions. (See also Separation of church and state and Laïcité.) In another sense, it refers to a belief that human activities and decisions, especially political ones, should be based on evidence and fact rather than religious influence.”
What I prefer is an understanding of meaning derived from the usage of a term. In American political usage, secularism predominantly refers to the second definition given above, so I tend to use the term in that sense, though of course using it to refer to a non-religious philosophy is not incorrect. Anyway, really just a tangent, since what I think is important is whether certain sorts of “spiritual” experiences are compatible with a Secular Humanist ideology. I happen to believe they are.
In answer to your question, I certainly think personal experiences such as you describe are often powerful and important. The question is what you do with them. When you use them to deepen the quality of your own experience of life and your relationships with others, they are very valuable. When you use them to serve as the basis for an understanding of the world which is then immune to contrary evidence, then they’re trouble. I think such experiences certainly are compatible with Secular Humanism, but I think we alwasy have to be on guard against overvaluing our own subjective impressions, since they are powerful in their impact on us out of proportion to their correspondence to any external reality.