The way I feel when the concept of a person in the abstract is invoked feels like a fainter version of the love I would feel towards a partner, a parent, a sibling, a child, a close friend, and towards myself. The feeling drives me to act in the direction of making them happy, growing their capabilities, furthering their ambitions, fulfilling their values, and so on. In addition to feeling happy when my loved ones are happy, there is also an element of pride when my loved ones grow or accomplish something, as well as fulfillment when our shared values are achieved. When engaging with the concept of abstract people, I can very easily imagine real people—each with a rich life history, unique ways of thinking, a web of connection, and so on...people who I would love if I were to know them. This motivates me to work hard to provide for their well being and growth, to undergo risks and dangers and sacrifices to protect them from harm, to empower and facilitate them in their undertakings, and to secure a future in which they may flourish—in the same ordinary sense that I imagine many other people do for themselves, their children and families, their tribes and nations, all people, all beings, and so on. I feel a sense of being united with all people as we work together to steer the universe towards our shared purpose.
You’ve italicized “effectively” as part of the question, but I don’t think I feel any real distinction between “wanting to help people” and “wanting to help people effectively”—when I’m doing a task, it seems like doing it effectively is rather straightforwardly better than doing it ineffectively. “Effective altruism” does imply a level of impartiality regarding who benefits which I don’t possess (since I care about myself, my friends, my family, and so on more than strangers), but it is otherwise the same. Even if I were I only to help people who I directly knew and personally loved in a non-abstract sense, I would still seek to do so effectively.